Calculating the Amount of Electricity Required to Discharge Cu Ions

To calculate the amount of electricity required to discharge a certain number of Cu ions, we need to consider the concept of Faraday's laws of electrolysis. Faraday's laws relate the amount of substance produced or consumed during an electrolysis process to the amount of electricity passed through the system.

1. Faraday's Laws of Electrolysis
Faraday's first law states that the amount of substance produced or consumed during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. Mathematically, it can be expressed as:

m = Z * F * Q

Where:
m is the amount of substance in moles
Z is the number of moles of electrons transferred per mole of substance (known as the stoichiometric coefficient)
F is the Faraday constant (96,485 C/mol)
Q is the total charge passed in coulombs

2. Determining the Stoichiometric Coefficient (Z)
In order to determine the stoichiometric coefficient (Z) for Cu ions, we need to examine the balanced chemical equation for the discharge of Cu ions. The balanced equation is:

Cu2+ + 2e- -> Cu

From the equation, we can see that 2 moles of electrons are required to discharge 1 mole of Cu ions. Hence, Z = 2.

3. Calculating the Amount of Charge (Q)
To calculate the amount of charge required to discharge 0.2 moles of Cu ions, we can rearrange the equation from Faraday's first law:

Q = m / (Z * F)

Substituting the given values:
Q = 0.2 moles / (2 * 96,485 C/mol)

Calculating Q:
Q = 0.2 / (2 * 96,485)
Q ≈ 0.000001036 C

4. Converting Coulombs to Other Units
If necessary, we can convert the charge in coulombs to other units such as milliampere-hours (mAh) or ampere-hours (Ah) using the following relationships:

1 C = 0.0002778 mAh
1 C = 0.0000002778 Ah

Conclusion
The amount of electricity required to discharge 0.2 moles of Cu ions is approximately 0.000001036 coulombs. This calculation is based on Faraday's laws of electrolysis, which relate the amount of substance produced or consumed during electrolysis to the quantity of electricity passed through the system. The stoichiometric coefficient for Cu ions in the balanced equation is 2, indicating that 2 moles of electrons are required to discharge 1 mole of Cu ions.